x-ray computer tomography is a specific layer recording method in which transversal cross-sectional images or a 3D volume image of the object area under examination are obtained. In this method the images represent the distribution of the linear attenuation coefficient for x-rays within an object area under examination and thereby a tissue density distribution within this area. The 2D or 3D images must be reconstructed in computer tomography from a large number of different projections. For this there are different reconstruction algorithms known for different beam geometries of the x-rays, for example the filtered back projection with 2D-parallel or fan beam geometry, specific algorithms for spiral computer tomography, approximative Feldkamp algorithm and generalizations thereof as well as exact reconstruction algorithms for 3D cone beam CT. With computer tomography 2D and 3D images from inside the body can be created with high spatial resolution of ≦1 mm and greater quantitative accuracy of the density resolution, typically in the range of a few Hounsfield Units (HU). The reconstruction algorithms used are all based however on idealized physical requirements in respect of the raw data or projection data recorded by the CT measurement system. In practice however, as a result of x-ray scattering and the effect of beam hardening, deviations from this ideal behavior occur which give rise to image artifacts in the reconstructed images. Examples of this are bar artifacts or shadow artifacts in the soft tissue between heavily-absorbent structures such as bones or metal implants. These artifacts in some circumstances adversely effect the quantitative accuracy and can thus lead to incorrect diagnoses.
To reduce or avoid these artifacts the application of post-reconstructive correction methods to the reconstructed image data is known. These correction methods only begin after image data has been reconstructed from the project data under idealized conditions. A significant procedural step with this correction method is the physical reprojection, also known as forward projection. With this reprojection the physical measurement method for obtaining radiographic projections is computationally remodeled in that each measurement beam, starting from the x-ray source, is followed through the object which has been approximated and discretized, i.e. broken down into pixels or voxels, through to the image detector and the contributions in the pixels or voxels lying along the way are summed to form the CT projection measured value. The reprojection differs here depending on the desired correction. Thus the reprojection to correct the beam hardening is performed with a different reprojection method based on another theoretical model for the underlying physical effect than the method for correcting x-ray scattering. Reprojection is thus the algorithmic implementation of a mathematical model for a physical effect. Physical reprojection allows the difference between idealized projection data without the physical disturbance effect, and real projection data to be computed. A correction image is then reconstructed from this difference data, through which, with an addition to the 2D or 3D image reconstructed under idealized conditions, a corrected image without the disturbing image artifacts is obtained. The correction cycle consisting of reprojection, difference formation and reconstruction to obtain a correction image can if necessary be repeated iteratively.